In the present study, improvement of numerical simulation code for the prediction of shock wave rise times developed by Swegle and Grady is carried out using equilibrium (thermoelastic) stress. The thermoelastic stress is obtained from Inside Temperature (IT) method for estimating temperatures in steady shock wave fronts established by Sano and Abe. In addition, use of the artificial viscous stress is limited conditionally in order to examine effects of the real shock viscous stress in our numerical calculation. The results of our improved simulation for 6061-T6 Al shocked below 9 GPa are compared with experimental results, and obtained good agreements. While, the effect of the viscous stress determined from the thermoelastic stress in the present method shows little differences from the Swegle-Grady method.